Degree

It is better to pass your class 12th with good grades and then focus for the IIT's and Iims that will be possible then only.

Hi,
You should complete your graduation first
This is the eligibility for AFCAT
Education: Graduation (min 3 years) in any discipline with min 60% marks and have passed Maths and Physics as subject at 10+2 level B.E/ B.Tech from a recognized University with min 60% marks. Age Limit : 20 to 24 years.

Check out IGNOU website. They might have good courses.

You cannot get a Bachelor's degree after class 10th. No recognized college in India provides such a programme.

You have to apply as foreign candidate in exam forms. Cost may be high for foreign nationals as compared to indian students. Mechanical engineering fee varies from college to college. If you are looking for government college, it may cost 20 k - 6 Lacs rupees. For private it may cost 5 - 10 Lacs. I will suggest you to give exams like JEE Mains for getting good government college.

Yes, you can apply as you are not having any Indian degree, so this will be easy for you to do it well.

Nothing is absolute right. Everything looks right in different dimensions. Most people will advice you do what you love. If you love it and have no interest in B.Tech then you can go for it. Some will advice you to complete your B.Tech and then go for it as you may loose interest in this also. According to my opinion, you should complete your B.Tech as it took effort and hard work to do uninterested things and if we can complete uninterested things, then we can surely do interested things. Every thing look awesome from outside. Rest your choice. Take any decision smartly and bravely.

Yes, this is possible. You can pursue the course.

The minimum eligibility criterion required for the candidates is to possess a Bachelor's degree in English or relevant discipline from a recognized university with a minimum aggregate score of 60%.

Eligibility for the exam Education : Graduation (min 3 years) in any discipline with min 60% marks and have passed Maths and Physics as subject at 10+2 level BE/ B.Tech from a recognised University with min 60% marks. Age Limit : 20 to 24 years.